theorem Th12:
  for U1,U2 be strict SubAlgebra of U0 st the carrier of U1 = the
  carrier of U2 holds U1 = U2
proof
  let U1,U2 be strict SubAlgebra of U0;
  assume the carrier of U1 = the carrier of U2;
  then U1 is strict SubAlgebra of U2 & U2 is strict SubAlgebra of U1 by Th11;
  hence thesis by Th10;
end;
